Question

Can someone explain this to me?
"If x is the first of two consecutive integers, express the sum of the two integers in terms of x. Simplify if possible."
I'm terrible with word problems, so I'm having a hard time understanding how the answer is "2x +1".

Answer 1

Since the first integer is "x", the second integer is one more than "x" since it is consecutive, so that next integer is "x + 1".

If you add them, you get:

x + (x + 1) = (x + x) + 1 = 2x + 1

Answer 2

All good now @SakuraAiken ?

Answer 3

Okay, yea, that actually is kinda making sense. Thank you :)

Answer 4

Good luck to you in all of your studies and thx for the recognition! @SakuraAiken

And you're welcome!

Answer 5

^.^; I thought I had it. It makes sense, but I just realized that I'm not sure how or where the "+1" comes from. How did you get the next integer "x+1"?

Answer 6

I tend to make things complicated sometimes, so thanks ahead of time for your patients.

Answer 7

If you have any integer, and let's call that integer "x", the very next integer is "1" greater than "x". Think of it as being one position "to the right" as you go to the right on a number line. You can conceptualize this by counting.

For example, if your number is "8", your next number, which is the next consecutive number is 1 greater. It is "9" and you can get that by counting and going ascending or bigger.

Answer 8

And don't worry about the content of your question. Sometimes, the fundamental abstract questions are the hardest, because everything after that depends on understanding the building blocks. Take your time. It's ok.

Answer 9

If you stop and think about it. it's possible that you're getting stuck on, not what is the next consecutive integer, but maybe on thinking of a number as "x" or any other variable. In this situation, you can think of "x" as a freely-chosen starting-point, that can be anything at all, but once its i chosen, it is a specific value. Then in your mind, you have to be able to say, "Ok, x was such-and-so, but now I want it to be something different." If you do that 3 or 4 more times, you will start to get a handle on what a variable is .

Answer 10

And while you are working on a problem, once you think of "x" as a starting-point, before you finish the problem, everything else in the problem is relative to where that "x" is. So, if you have an integer "x", to get to the next number, you have to "start" at "x" and go "one more", so you have "x + 1" which is "start at x and add 1".

Answer 11

Honestly I'm not always sure where I get stuck in math sometimes, but I usually continue to have a hard time until I figure out the process for getting the answer, even if I know what the answer is. If I know how to GET the answer, then I can use the same process in similar problems and then be able to solve them myself. I'm trying to read the explanation in my book as well as ask for advise. I've got like 40-50 beginning algebra or algebra word problems to get done before wednesday and I don't knw how I'm gonna do it XD

Answer 12

when a word problem calls for being turned into a math problem, I get stuck at figuring out how to write it as a math problem.

Answer 13

That's a lot of problems. And what is really needed here, as I'm sure you know, is not reaaly the answers, but the understanding and methodology. I have 2 good suggestions for you to get you going fast and well. Probably the best tutor here is Jim Thompson. He's ranked at 99, so you can always find him when doing "home" and seeing him near or at the top. His handle is something like "jim_thompson5910" or something like that. Contact him. He's incredibly good because he is highly experienced in tutoring all levels and knows how to get fundamentals across better than anyone I know. He also does live tutoring. Which comes to my second suggestion. A live tutor will probably help a LOT. As a third suggestion. You can work with tutors like me who know math well, but are not trained in math education.

Answer 14

I'll keep that in mind, thanks :)

Answer 15

There is a whole completely different area of expertise with math education training. It's worlds different from becoming a mathematician. I rely on whatever insight I can bring to the table and my level of patience and understanding. I have a college degree in math, but that is not what is needed here between me and you or between you and any other tutor. You need someone who relate the fundamentals. I can do that to a certain degree, or so I've been told. But it's up to the student and everyone learns differently. I tend to be abstract in my teaching and if someone learns more concretely, then I'm not the best tutor for that person.

Answer 16

I'm going to try something here and I'm going to draw a picture. You can tell me if this helps at all.

Answer 17

looks a little like what's in my book. I'm trying to apply it to my math problems at the moment. I'm a little slow at it still though, but so far so good I think.

Answer 18

You sort of think of that "x" as a "shift". Sort of like a shifted "0". If you look at the "0", then "IN RELATION" to that "0", you can see that "-1" is "0 - 1" and "2" is "0 + 2". It the same with "x". Everthing around it can be expressed in terms of "x". Either a little subtracted from it or added to it.

Answer 19

Another problem here in my book is worded a little different. it says "If x is the first of three consecutive even integers, write their sum as an algebraic expression in x." is expressing the sum of integers in terms of x the same type of thing as writing the sum of integers as an algebraic expression in x?

Answer 20

and would the answer be 3x+3?

Answer 21

Yes, it is. It is that way because what makes this algebra is questions and answers being expressed in terms of general quantities, not as specific quantities. That's represented by the use of variables. It's a way of saying "this problem at hand works for all numbers." Or for all integers or for postitive integers. Whatever x is defined to be.

And in answer to your last question, you are absolutely right! Great job!

The way I did it was:

x + (x + 1) + (x + 2) = (x + x + x) + (1 + 2) = 3x + 3

which is probably similar to the way you did it.

Answer 22

yea, I wrote "x+(x+1)+(x+2)

Answer 23

Now, remember what I said about Jim Thompson and the tutors that have a high "Smartscore". They're all good, but some are better than others. Look for the ones who will spend time. I threw that in because my computer is going haywire and I don't know how long this session will last before it goes really funny.

Answer 24

k, how can I find him on openstudy?

Answer 25

and thank you so very very much for all the time you've spent helping me :)

Answer 26

I'm going to leave this session, but hang on and I'll be RIGHT back. I can no longer have more than one window open, so it will look like I disappeared, but I'm coming back. I want to get the right spelling on his handle. If my computer doesn't let me come back, you hit the "home" button near the top center-right and look to see if he's online.

And you are a pleasure to work with. I'll look for you when I can.

Answer 27

I made it back! My computer needs a life-jacket! I sent you a message with good info. @SakuraAiken

Answer 28

lol welcome back! I just responded and added a question to your message XD

Answer 29

So, here's a couple other good tips, aside from the math and more about Openstudy. It's good to start a new problem thread with each question, especially if you have only one tutor helping you and it's not going so well. Starting a new thread will attract new and multiple tutors. Find "favorite" tutors and fan them to know when they are on-line and hound them. If no one is answering your question, put it to the top of the question heap. And for now, I'll try to help, but you might want to start doing new threads even now. Try to catch the eye of those tutors I mentioned. Message them. Invite them. Bug them.

Answer 30

k

Answer 31

The sum of an integer and the third in a string of 4 consecutive integers is exactly what you thought it was:

2x + 2

Because you have a string looking like:

x, x+1, x+2, x+3

and you are adding x and (x + 2) to get the expression:

x + (x + 2) = (x + x) + 2 = 2x + 2

So you were right! Good job again!

Answer 32

Now, seriously, start a new message before asking your next question, because you want to get a bunch of helpers. Multiple input is good at this stage.

Answer 33

k, do I have to close this one out to start a new one?

Answer 34

It's good to close out the questions. I don't know if it's required, but it's probably a really good thing to do.

Answer 35

If you put something like "Help!" in the title, that probably helps a lot too.